Consider an engineer who will visit twenty manufacturing facilities in a single week, and must select a visitation order. Eighteen facilities are production facilities and two are packaging facilities (facilities of the same type are indistinguishable).

Suppose the visitation order will be chosen randomly (i.e., the next facility to be visited is always chosen randomly among those that have not yet been visited). What is the probability that engineer visits at least one production facility between visits to the two packaging facilities?